Department of Preventive Medicine and Biostatistics (OEHS)
11/10/22
Lesson Objectives
Explain rational for the use of probabilistic risk assessment
Describe the tiered approach for risk assessment
Understand the basics of Monte Carlo sampling
Discuss the advantages and disadvantages of using probabilistic assessments compared to deterministic assessments
Probabilistic Risk Assessment
“An analytical methodology used to incorporate information regarding uncertainty and/or variability into analyses to provide insight regarding the degree of certainty of a risk estimate and how the risk estimate varies among different members of an exposed population…”
A group of techniques that incorporate uncertainty and variability into risk assessments
EPA, 2014 Risk Assessment Forum White Paper
Variability and Uncertainty Review
Variability: the inherent natural variation, diversity and heterogeneity across time, space or individuals within a population or lifestage
Uncertainty: imperfect knowledge or a lack of precise knowledge of the physical world, either for specific values of interest or in the description of the system
Probabilistic Approach - Motivation
Risk assessors, risk managers and others, particularly within the scientific and research divisions, have recognized that more sophisticated statistical and mathematical approaches could be utilized to enhance the quality and accuracy of Agency risk assessments
Various stakeholders, inside and outside of the Agency, have called for a more comprehensive characterization of risks, including uncertainties, to improve the protection of sensitive or vulnerable populations and lifestages
EPA, 2014 Risk Assessment Forum White Paper
Deterministic: Point Estimate of Exposure Dose
Deterministic risk assessments express health risks as a single numerical estimate of risk
Assuming reasonable maximum exposure
Compounds unrealistically high estimates
Difficult to know/communicate the level of conservatism
Assuming average exposure
May present unacceptable risks
Mostly qualitative assessment of uncertainty and variability
Tiered Approach for Risk Assessment
Assessments that are high in complexity and regulatory significance benefit from the application of probabilistic techniques
Intergovernmental Panel on Climate Change: probability density function analysis of radiative forcing
Computer graphics: Path/ray tracing renders a 3D scene by randomly tracing samples of possible light paths
US Coast Guard: computer modeling software SAROPS calculates the probable locations of vessels during search and rescue operations
Monte Carlo Simulation: IPCC (WG1AR5)
Monte Carlo Simulation: IPCC (WG1AR5)
Monte Carlo Simulation: IPCC (WG1AR5)
Monte Carlo Simulation: SAROPS
Search and Rescue Optimal Planning System (SAROPS)
Software used by the U.S. Coast Guard for Maritime Search Planning
SAROPS is a Monte Carlo based system that uses thousands of simulated particles generated by user inputs in a wizard based Graphical User Interface
Handle multiple scenarios and search object types
Model pre-distress motion and hazards
Account for the affects of previous searches
Monte Carlo Simulation: SAROPS Screen
Monte Carlo Simulation: Step 1
Set up the predictive model, identifying both the dependent variable to be predicted and the independent variables (also known as the input, risk or predictor variables) that will drive the prediction.
Specify probability distributions of the independent variables
Use historical data and/or the analyst’s subjective judgment to define a range of likely values and assign probability weights for each.
Probability distribution: mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment
Type of distribution is useful when you need to know which outcomes are most likely, the spread of potential values, and the likelihood of different results
Selection of the appropriate distribution depends on the presence or absence of symmetry of the data set with respect to the mean value
library(tidyverse)library(mc2d)# Define variables and distribution parametersc <-0.00375# concentration (mg/L) c_p1 <-0.00375# concentration mean c_p2 <-0.001# concentration s.d.ir <-1# ingestion rate ir_p1 <-0.5# ingestion rate minimum ir_p2 <-1# ingestion rate mode ir_p3 <-5# ingestion rate maximumef <-350# exposure frequency (days) ef_p1 <-200 ef_p2 <-350 ef_p3 <-365ed <-6# exposure duration (days)bw <-70# body mass (kg)bw_p1 <-70bw_p2 <-75at <-365*70# averaging time (days)csf <-1.5# cancer slope factor## Deterministic# Daily Intake = (C x IR x EF x ED x) / (BW x AT) Risk = CSF x (C x IR x EF x ED x) / (BW x AT)daily_intake <- (c * ir * ef * ed) / (bw * at) daily_intake
[1] 4.403131e-06
risk <- csf * ((c * ir * ef * ed) / (bw * at)) risk
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.732e-06 6.197e-06 9.269e-06 1.051e-05 1.343e-05 5.828e-05
EPA Case Study
Probabilistic Risk Analysis of Exposure to Polychlorinated Biphenyls via Consumption of Fish From a Contaminated Sediment Site
EPA Region 2 conducted a preliminary deterministic HHRA at the Hudson River PCBs Superfund site
Consumption of fish provided the highest exposure among relevant exposure pathways
Cancer risks and noncancer health hazards exceeded regulatory benchmarks
EPA Case Study: Analysis
Monte Carlo analysis of the variability of exposure as a function of the variability of individual exposure factors
Mathematical models of the environmental fate, transport and bioaccumulation of PCBs in the Hudson River previously developed were used to forecast changes in PCB concentration over time
Monte Carlo results consistent with deterministic results